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在线张量学习：计算与统计权衡、自适应性及最优遗憾AI 解读

Large tensor learning algorithms are typically computationally expensive and require storing a vast amount of data. In this paper we propose a unified online Riemannian gradient descent (oRGrad) algorithm for tensor learning, which is computationally efficient, consumes much less memory, and can handle sequentially arriving data while making timely predictions. The algorithm is applicable to both linear and generalized linear models. If the time horizon T is known, oRGrad…

计算高效且统计最优的稳健高维线性回归AI 解读

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since the robust loss functions are usually nonsmooth. More recently, computationally fast nonconvex approaches via subgradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even…

快速黎曼优化下的广义低秩加稀疏张量估计AI 解读

We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by the low-rank part. The framework flexibly covers both linear and generalized linear models, and can easily handle continuous or categorical variables. We propose a fast algorithm by integrating…